Terahertz systems, or systems operating in the terahertz frequency range from approximately 100 GHz to 10 THz, are increasingly employed in various applications. Among the first of such applications include bio-spectroscopy and molecular spectroscopy applications. More currently, terahertz systems are increasingly being employed in imaging applications, compact range radars and remote sensing applications. The solid-state realization of such systems, as well as the terahertz sources, have typically been built using heterojunction bipolar transistor (HBT) and high electron mobility transistor (HEMT) technologies, based on III-V semiconductors, or semiconductors comprising Group III and Group V elements, such as GaAs. As the complementary metal-oxide semiconductor (CMOS) technology scales down, the maximum operating frequency, fmax, of the transistors reach the lower end of the terahertz range. For example, 65 nm CMOS technology has already reached an fmax of approximately 200 GHz. The downscaling of CMOS technologies along with the drawbacks in cost and efficiency that are associated with III-V semiconductor technologies have inspired more recent terahertz work in silicon processes.
In order to realize terahertz systems using integrated circuits, solid-state terahertz sources having nonlinear elements may be used for up/down conversion and multiplications to generate power. However, the use of nonlinear devices may generate undesirable harmonics which adversely affect the resulting spectrum. Accordingly, high quality factor filters are used to suppress such harmonics. In terahertz spectroscopy, for instance, a high quality factor filter bank is used to find the output spectrum. This is typically done off-chip by mixing down the signal and using the filter bank at low frequencies. In order to eliminate the mixer and make a silicon-based spectrometer, a high quality factor filter at terahertz frequencies is desirable. However, the quality factor of conventional passive filters is limited to the quality factor of the individual components. As such, the quality factor is low at high frequencies due to ohmic and substrate losses in the associated silicon processes.
Optical prisms with high quality factor filters and demultiplexers have also been realized using, for instance, photonic crystals. In particular, the frequency bandgap of the photonic crystals are engineered to provide a spatial filter, or a superprism, such that different frequencies of a signal propagate in different directions within the crystal. Here, the principle is to employ a periodic structure, such as high-pass two-dimensional (2D) metamaterial lattices, to create a bandgap, and thus, to direct energy through the medium as a function of the signal frequency. However, the light propagation in such crystals is comparable to that found in a diffraction grating, and thus, the dispersion that causes the superprism effect originates from scattering.
In light of the foregoing, there is a need for an apparatus and method for providing a filter for millimeter-wave and terahertz frequencies which exhibits a quality factor that is substantially greater than those of the individual components thereof. Moreover, there is a need for a high quality factor filter that exhibits a negative effective index, directs energy flow as a function of signal frequency at frequencies close to the cut-off frequency, and channels signals from an input to an output.